Stress field near the mixed mode crack tip under plane stress conditions

Abstract

The asymptotical solution to the problem of the mixed loading of the cracked specimen under plane stress conditions in materials with fractional-linear constitutive relations of steady -state creep is given. The stresses and creep strain rates in the vicinity of the mixed mode crack tip are obtained. The type of mixed loading is specified by the mixity parameter which is varying from 0 (this type of loading corresponds to pure shear) to 1 (the loading corresponds to tensile loading). The analytical presentation of the stress and the creep strain rate fields is found for all values of the mixity parameter. It is shown that the stress field consists of different regions inside which the stress components are determined by different formulae. The boundaries of the regions are found numerically. The comparison of the analytical solution with the numeric solution obtained for the power-law material for large values of the exponent n is given.

Keywords

• mixed mode (mode i + mode ii) loading
• asymptotical analysis
• the near crack-tip stress field
• analytical solution
• analytical presentation of the stress field near the crack tip